Yoda wanted to beat Palpatine, but he failed. And the situation became worse due to the new Galactic Empire having enormous resources, including a clone army which two Jedi couldn't beat.

So Yoda and Kenobi went into exile until the right time. They had two force-sensitive babies, one of which was the hope. Yes, in the end of episode III, they were escaping to survive (thanks to @PaulD.Waite for pointing it out). But, they stick to this thing for decades.

Let's look at another option. Order 66 didn't kill all force-sensitives from the Galaxy. There were still hundreds of survivors. They could have united them to create an army of force-sensitives. Plus, with their military experience, they could have nurtured budding rebel alliances.

Instead they wasted their time in the hope of producing good powerful Jedi. Is there any in-canon answer explaining what made Yoda and Kenobi thought that adding one or two Jedi to their side could beat The Galactic Empire?

why were there not more Jedi? for the sake of the plot of course :P!
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IamVeryCuriousIndeedJun 28 '14 at 21:30

It's a reasonable question but any answer is going to be pretty darned opinion-based. The best I can do is that he probably foresaw (with his jedi powers) that he and Obi Wan needed to hide until the time was right...
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Richard♦Jun 28 '14 at 21:32

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And just to query the premise, because I don’t remember Revenge of the Sith very well: “Yoda and Kenobi went into exile until the right time”. Was it clear at the end of Revenge of the Sith that they had a plan to fight the newly-formed Empire? Weren’t they just running at that point, trying to avoid being slaughtered like the rest of the Jedi?
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Paul D. WaiteJun 28 '14 at 22:23

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@PaulD.Waite - a force-sensitive is merely someone who has some affinity for the force, and may be able to be a Jedi (or Sith). Without training, there is little that a force-sensitive could do, however.
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SSumnerJun 28 '14 at 22:25

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@PaulD.Waite you might consider asking "What does Force sensitivity mean?" as its own question. It certainly has a long enough answer. Let me suffice it to say that untrained (in the Force) force sensitive individuals could be worth more than 10 highly trained and well equipped commandos, but a Sith lord would be willing to sacrifice thousands of such commandos for an incredibly weak force sensitive. (Darth Bane Path of Destruction). So training that many in secret for years would be an issue esp bc Palpatine was searching for those people and the remaining Jedi.
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Thoth19Jun 29 '14 at 3:07

4 Answers
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While the previous answers are all very good, they fail to note the added information from the novelisation of Revenge of the Sith. The novel makes it clear that the duel between Palpatine and Yoda is NOT a draw, as it appears in the film, but that Palpatine mops the floor with his "little friend." While I do not have the text with me to quote it properly, if someone else can track it down, feel free to edit it in.

Yoda essentially realised that "the Sith had changed." The Jedi, for a thousand years, had stagnated as an order, comfortable in their position. The Sith, however, forced underground after their defeat at the hands of the Jedi, had adapted to their new situation, spending a thousand years systematically preparing for their return to power. The Jedi had been unable to prepare for this, as they only had rumours of the Sith's continued existence and knew nothing of their new abilities and methods.

After his defeat at the hands of Sidious, Yoda recognised that the Jedi also needed to evolve and adapt if they were to survive. You'll note that he concentrated on different skills when training Luke than were the norm in the old Jedi Temple; the physical training was emphasised, to the point that Luke was shown, in Dark Force Rising, to have no training whatsoever in the conflict-resolution aspects of being a Jedi (unless, of course, one considers whipping out the lightsaber and going to town conflict resolution. I would). That aspect of a Jedi's training was considered so important that they open The Phantom Menace with, as well as numerous Expanded Universe material. Luke was not given any training at all, and acknowledges that even Han would have done as well as he did.

Luke's training was specialised, apparently with the specific goal of killing Palpatine and/ or Vader. He even acknowledges, in The Black Fleet Crisis trilogy (I don't recall which book, though I think it may have been the first one Before the Storm) that he was fashioned as a weapon.

Interesting. Although if Luke was a weapon, he was nowhere near ready to face the Emperor in combat. As the Emperor said, "your feeble skills are no match for me, boy!" If Yoda's ghost had been watching, he would have thought, "Hmmm. Taught him defence from Force lightning, maybe I should have."
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Royal Canadian BanditJun 29 '14 at 10:30

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"(unless, of course, one considers whipping out the lightsaber and going to town conflict resolution. I would)." I call it aggressive negotiations.
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Niet the Dark AbsolJun 29 '14 at 11:16

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@RoyalCanadianBandit: It's possible that Luke taking off to fight Vader on Bespin ruined that part of the plan. Or that he was intended merely to kill Vader, perhaps with Yoda himself assuming he'd live longer and get another crack at Palpy himself.
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James SheridanJun 29 '14 at 12:02

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@JamesSheridan: I think the first is more likely. At the end of TESB he was helpless against Vader, let alone the Emperor, so it explains why Obi-Wan and Yoda tried so hard to talk him out of going.
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Royal Canadian BanditJun 29 '14 at 19:59

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@RoyalCanadianBandit: I agree entirely. Yoda's plan seemed to be to train Luke into the ultimate Jedi weapon, then let him loose on Vader and Palpatine. He obviously wanted to proof him against the Dark Side as well - hence the scene in the Dark Side cave - but what other Jedi skills beyond those required for combat would be taught to Luke is up for debate. My own theory is that Yoda would sic Luke onto the Sith like a mad dog, then reel him back in and teach him the rest of the Jedi ways once they were dead. Or perhaps he always planned to let Luke learn other skills on his own.
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James SheridanJun 30 '14 at 2:58

The only firm in-canon mention I can find is Yoda's statement to Bail Organa near the end of the Revenge of the Sith film:

Into exile I must go. Failed, I have.

It makes sense that he would feel this way, as he tried to confront Darth Sidious, but was unable to defeat him. Presumably, he saw no way to defeat the empowered Sith anytime soon.

Personality-wise, Yoda was not an impulsive Jedi, nor was he a front-line 'soldier' (despite him being a Swordmaster) - he was a wise teacher. Thus, with the Skywalker twins being 'spirited' away into hiding, he could see that their best chance was to wait.

The prophecy of the Chosen One was seen by many as being Anakin Skywalker - and in the end, of course, it was. But when he fell to the dark side to become Darth Vader, no doubt Yoda questioned it, especially when he was becoming less believing in the possibility of redemption for fallen Jedi. So, while there were certainly other Force-sensitives out there, it seems likely that he would wait for the time when the children of Anakin, themselves highly likely to be strong in the Force, were able to take a role in the opposition.

When Yoda went into exile, there is no doubt that he knew this battle was not to be won by strength against strength. And indeed it was not. The new Galactic Empire controlled hundreds of star systems, and had a new massive Army and Navy. The new Emperor Palpatine had enough control and power to squash less powerful Force users, and as showed later, the ability to ferret them out. Yoda and Obi-Wan understood that this was tomorrow's battle, not today's.

And so in the end, Yoda's work proved vital. He helped to train a great Jedi in Luke Skywalker, and that was one of the key movements that brought down the Empire. In letting Leia work through different channels, she was able to be an instrumental member of the Alliance, and was again, very instrumental in bringing down the Empire. So while we can't say for certain everything worked out exactly as Yoda planned, 'history' vindicates his choices. And I'm sure if you were to ask him what exactly his plans were after Episode III, he would probably respond...

Honestly, the key moment is when Vader saw his son being tortured, and had the means, motive and opportunity to toss Palpatine over the chasm. Yoda and Kenobi's plan was for Luke to kill Vader, they considered turning him impossible. It was Luke's plan alone to turn him. Really, whoever decided "The throne room ought to have a miles long shaft in it" sealed the fate of the Empire. Vader likely could not have killed him in a prolonged duel.
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swbarnes2Jun 29 '14 at 19:52

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"Vader likely could not have killed him in a prolonged duel." Maybe, maybe not. They never dueled...ever, so we'll never know.
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Paul DraperJun 29 '14 at 21:21

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Why didn't Yoda take Luke with him to train him from birth? The Empire didn't find Yoda during his exile, so it would stand to reason him taking Luke with him would've provided 2 decades worth of upbringing and training in the Force. Would the Emperor really have been able to sense something and find them?
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TheCleanerJun 30 '14 at 15:58

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@TheCleaner: For one thing, a swamp is hardly the place to raise a child. Yoda may also have feared that the children of Skywalker would take after their father, in which case NOT training them would be very good for the galaxy. If one accepts the EU material about the reason Yoda stayed on Dagobah - the Dark Side Cave hid his presence - then this makes sense; two or three Jedi are a lot harder to hide than one.
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James SheridanJul 23 '14 at 0:18

The key point is that Luke is not just any Force-sensitive. He is a Force prodigy, equal in potential to Anakin before his fall. He can accomplish things which an army of lesser Jedi could not.

This is supported by several remarks in the films.

Darth Vader, TESB:

You can destroy the Emperor. He has foreseen it.

Obi-Wan Kenobi, ROTJ:

The Emperor knew, as I did, that if Anakin had any offspring, they would be a threat to him.

Yoda, TESB:

(Referring to Luke) Only a fully trained Jedi, with the Force as his ally, will conquer Vader and his Emperor.

The remaining Jedi and Sith all recognised that Luke would be the key to overthrowing the Empire. No doubt this was reinforced by their ability to see the future, hazy though it was.

Accordingly, protecting and training Luke had to be the priority. Obi-Wan and Yoda could not afford to risk themselves by trying to hastily recruit and train lesser Jedi.

Instead, like the true martial arts masters they are, the Jedi waited patiently and used the Empire's strength against it. Over time, Imperial oppression motivated more and more systems to join the Rebellion.

As Leia puts it in ANH:

The more you tighten your grip, Tarkin, the more star systems will slip through your fingers.

Organising a military and political rebellion was important, but they left that in the capable hands of Bail Organa and later of Princess Leia.

Two decades later, the Rebellion had grown to the point where it could seriously challenge the Empire, and Luke was old enough to fulfill his destiny. How much of this was deliberate planning, and how much was sensing the right course of action through the Force, we cannot say, but it did succeed in the end.

Only a fully trained Jedi, with the Force as his ally, will conquer Vader and his Emperor. ~> Wasn't Yoda himself fully trained?
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SS-3.1415926535897932384626433Jun 29 '14 at 4:34

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@SachinShekhar: Of course he was, but even he failed to approach Vader in power, whereas Luke - and by supposition, Leia - were equal in power to Vader. Yoda had already failed to defeat Palpatine, whereas Vader might have had the capacity. Presumably, Luke/ Leia would also have that capacity.
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James SheridanJun 29 '14 at 6:32

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I fail to see how a "summer camp" at Dagobah equals to "fully trained"
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SJuan76Jun 29 '14 at 9:40

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@SJuan76: I'm pretty sure Yoda and Obi-Wan felt the same. Hence them crapping themselves and tripping over each other to give Luke last minute warnings when he insisted on leaving Dagobah to fight Vader before he was ready.
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James SheridanJun 29 '14 at 12:03

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@SJuan76, it doesn't. And so Luke got his a** (arm) handed to him.
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Paul DraperJun 29 '14 at 21:18

At the time of Order 66 ANY force sensitives were being hunted down. If identified they would've been killed or turned. Hiding was the only choice not just for Yoda and Obi Wan, but others as well. Either denouncing their Jedi heritage and living incognito, or just disappearing. There was no real way to organize any kind of rebellion at the time, as all powerful Jedi were killed, and any that were in training lacked the skill or experience to make a difference. The new show "Rebels" will probably show the infantile stages of the rebellion, but even then it took years.

Specifically you might want to mention the specifics of Starkiller, Mara Jade, etc. Organizing a rebellion would also be difficult because at that time the Storm Troopers were clones and answered only to Palpatine, whereas later they had regular organics which diversified, but weakened them.
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Thoth19Jun 29 '14 at 3:10

My question mentions that they stick to the hope plan for decades. By the time, rebel alliances started to show up, they could have come out and do some productive jobs.
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SS-3.1415926535897932384626433Jun 29 '14 at 4:29

@SachinShekhar: Training Luke was the single most productive job they could do. It was Luke, after all, whose actions led to the deaths of both Palpatine and Vader.
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James SheridanJun 29 '14 at 7:00